Question: $\dfrac{ 7g + 9h }{ 9 } = \dfrac{ 5g - 3i }{ 9 }$ Solve for $g$.
Solution: Notice that the left- and right- denominators are the same $\dfrac{ 7g + 9h }{ {9} } = \dfrac{ 5g - 3i }{ {9} }$ So we can multiply both sides by $9$ ${9} \cdot \dfrac{ 7g + 9h }{ {9} } = {9} \cdot \dfrac{ 5g - 3i }{ {9} }$ $7g + 9h = 5g - 3i $ Combine $g$ terms on the left. ${7g} + 9h = {5g} - 3i$ ${2g} + 9h = -3i$ Move the $h$ term to the right. $2g + {9h} = -3i$ $2g = -3i - {9h}$ Isolate $g$ by dividing both sides by its coefficient. ${2}g = -3i - 9h$ $g = \dfrac{ -3i - 9h }{ {2} }$